Aqueous salt solutions containing elongated micelles of sodium dodecyl sulfate (SDS) have been studied at 45 degreesC using small-angle neutron scattering. At NaCl concentrations in the 1-2 M range, the scattering data are consistent with semiflexible rather than rigid rodlike micelles, and this conclusion is consistent with previous studies of SDS micelles using small-angle scattering. However, until now quantitative determinations of micellar flexibility, that is, of persistence lengths, especially as a function of ionic strength, have not been available. By making measurements in the range of scattering vectors appropriate for this length scale and by incorporating the effect of intermicellar interactions into the fitting protocol, it has been possible to determine persistence lengths accurately. Partitioning of the values into intrinsic and electrostatic components is discussed, and the results are compared with data for the highly flexible anionic polyelectrolyte sodium polystyrenesulfonate. The one-dimensional bending moduli for the flexible SDS micelles are compared to the analogous two-dimensional bending moduli for SDS bilayers.